JENSEN, RICHARD; PHD
NORTHWESTERN UNIVERSITY, 1980
ECONOMICS, THEORY (0511)
Optimal behavior of a firm toward an exogenously developed innovation of uncertain
profitability is
examined. It is shown that a firm may delay adopting a profitable innovation
if it is uncertain about the
innovation's profitability but can reduce the uncertainty by waiting and gathering
information. The
decision problem is formalized as an optimal stopping problem in which at each
decision date the firm can
either adopt or wait and take an observation. The firm starts with a subjective
probabilistic belief that the
innovation will be profitable which is updated according to generalized learning
rules after each
observation. The optimal decision rule can be characterized by a unique reservation
probability
representing the minimum value which the firm's current (updated) belief that
the innovation will be
profitable must attain to induce adoption. When a delay in adoption occurs,
that delay will be longer when
the firm's original belief is smaller, the information received is less favorable,
the ability to learn is
unlimited, and the expected profitability is lower. An industry model in the
absence of rivalry is
constructed in which firms are Bayesian learners and are identical in all respects
except for their original
beliefs. When these beliefs are distributed uniformly over the unit interval,
the expected diffusion curve
will be either S-shaped or concave. Rivalry is examined in a duopoly model in
which the existence of a
Bayesian (fulfilled expectations) equilibrium is proved. In it each firm accurately
and endogenously
estimates the probability of adoption by the rival. Adoption by one firm need
not increase the probability
of adoption by the other firm. These last two results raise serious questions
about the assumptions
commonly made in empirical studies of diffusion.
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